The in-plane distribution of density in handsheets

1. The in-plane distribution of density in handsheets C.T.J. Dodson, Y. Oba and W.W. Sampson On the distributions of mass, thickness and density of paper Appita J. 54, 4 (2001) 385-389.

2. Overview • Introduction • Measurements • Theory • Conclusions

3. Formation - Distribution of Mass Density Affects pore size distribution, ink transfer, strain distributions under tension, etc.

4. Distribution of Density • Many physical properties, e.g. tensile index, • tear index, light scattering coefficient, • permeability, etc. are strongly correlated • with mean sheet density. • Expect therefore that the local properties of • small zones will be dependent on local • density.

5. Experimental • Sheets with a range of structures • and known forming conditions. • Measure thickness and grammage • of small zones knowing the position • of each measurement.

6. 48 conditions

7. Non contacting double laser • triangulation thickness tester • Computer controlled x-y stage • 0.5 mm pitch. Local average • thickness of 1mm square zone • taken as average of 4 measure- • ments • Samples marked 1 mm Local thickness determination

9. Local grammage determination • Ambertec b-formation tester. • Same 1 mm zones measured • as for thickness. • Formation at scales between • 100 mm and 7 mm measured.

10. grammage thickness  density

15. Thickness, mm Grammage, g m-2

16. If thickness and grammage are bivariate normally distributed we have: where and if Theory

21. Conclusions • Coefficients of variation of thickness • and grammage are linearly dependent and • independent of furnish. • Bulk structure dominated by presence of • TMP in blended furnish. • Mean thickness depends on formation.

22. Relationship between local grammage • and thickness is well described by • the Bivariate normal distribution. • An approximate model slightly under- • estimates density variation.

23. Acknowledgments Funding: Oji Paper Company Ltd., Japan